Memory coherence of a sympathetically cooled trapped-ion qubit

We demonstrate sympathetic cooling of a ⁴³Ca⁺ trapped-ion ``memory'' qubit by a ⁴⁰Ca⁺ ``coolant'' ion sufficiently near the ground state of motion for fault-tolerant quantum logic, while maintaining coherence of the qubit. This is an essential ingredient in trapped-ion quantum computers. The isotope shifts are sufficient to suppress decoherence and phase shifts of the memory qubit due to the cooling light which illuminates both ions. We measure the qubit coherence during ten cycles of sideband cooling, finding a coherence loss of 3.3% per cooling cycle. The natural limit of the method is O(10^-4) infidelity per cooling cycle.